3(t^2+4)=20t

Solution for 3(t^2+4)=20t equation:

Simplifying
3(t2 + 4) = 20t

Reorder the terms:
3(4 + t2) = 20t
(4 * 3 + t2 * 3) = 20t
(12 + 3t2) = 20t

Solving
12 + 3t2 = 20t

Solving for variable 't'.

Reorder the terms:
12 + -20t + 3t2 = 20t + -20t

Combine like terms: 20t + -20t = 0
12 + -20t + 3t2 = 0

Factor a trinomial.
(2 + -3t)(6 + -1t) = 0

Subproblem 1
Set the factor '(2 + -3t)' equal to zero and attempt to solve:

Simplifying
2 + -3t = 0

Solving
2 + -3t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3t = 0 + -2
-3t = 0 + -2

Combine like terms: 0 + -2 = -2
-3t = -2

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {0.6666666667, 6}